Both countries, warming up for the Copa America in Argentina in July, fielded teams made up of home-based players which in Argentina's case is virtually a third string.
Hauche opened the scoring in the ninth minute and added the third just before halftime following a fine run down the right by his Racing Club team mate Ivan Pillud, who beat two defenders before crossing from the goal-line.
Striker Pablo Zeballos equalised for Paraguay in the 14th minute with a shot that took a deflection and central defender Federico Fernandez restored Argentina's lead in the 37th, heading home a free-kick by midfielder Diego Valeri.
Defender Elvis Marecos reduced the deficit 11 minutes into the second half when he headed a corner inside the near post from a corner.
Winger Enzo Perez added Argentina's fourth in the 74th.
Argentina coach Sergio Batista has picked an intermediate squad of foreign-based players on the fringe of his first team for a tour of Nigeria and Poland next month as he looks to settle on his 22 players for the Copa America.
The squad, to meet Nigeria in Abuja on June 1 and Poland in Warsaw four days later, includes the likes of Manchester City's Pablo Zabaleta, 2010 World Cup defender Nicolas Otamendi of Porto and Palermo playmaker Javier Pastore.
